石墨烯中分数量子霍尔效应的研究

In this project, we study fractional quantum Hall effect (FQHE) in graphene using numerical methods, such as exact diagonalization and density matrix renormalization group. Considering the unique properties of graphene material, the effects on FQHE from Landau-level mixing, disorder scattering, and anisotropic interaction are not negligible. For these complicate factors, our research is focused to develop proper theoretical model frames and to propose sets of feasible numerical approaches so that we can investigate the properties of the ground state and low-energy excitations in the graphene FQHE system under these effects. This would also provide us with the possibility to explore exotic quantum states in such system. Our work is expected to be used for the better explanation on the experimental observations and to supply theoretical guidance for novel electronic devices in future.

运用严格对角化以及密度矩阵重整化群等数值计算方法我们对石墨烯薄膜材料中的分数量子霍尔效应进行研究。由于石墨烯材料的特性，朗道混合、杂质散射、相互作用各项异性等因素对分数量子霍尔效应体系的影响不容忽视。针对这些复杂效应，我们的研究侧重于发展出适合的理论模型框架和建立一套切实可行的数值处理手段，对受影响的石墨烯分数量子霍尔效应系统的基态和低能激发性质进行研究，并探索新型量子相态的可能性。我们的研究预期将为实验观测和未来新型电子器件的设计提供理论基础。